The Border Reivers star underwent surgery on the damaged left shoulder in Glasgow on Sunday afternoon and has been told to expect a lengthy spell on the sidelines.
Scotland team doctor James Robson said: "Surgeon Gordon McKay has repaired damage to a number of structures within the joint.
"Chris will now begin a period of rehabilitation. Recovery from an injury of this nature can take three to four months."
Johnnie Beattie was also injured during the match at Murrayfield, suffering ankle ligament damage.
And uncapped duo Rory Lawson and Alasdair Strokosch have been added to the Scotland squad for Saturday's second Test against Australia as injuries mount up.
Gloucester scrum-half Lawson will replace Cusiter, while Edinburgh Rugby's back-row forward Strokosch takes the place of Beattie.
Allister Hogg has already been ruled out, while captain Jason White waits anxiously on a further assessment of the knee injury sustained during the 48-6 win over Romania a week ago.